《多元统计分析》Chapter 7 Discriminant Analysis （判别分析）

Chapter 7 Discriminant Analysis (判别分析)

zf Chapter 7 Discriminant Analysis (判别分析）

Presentation Outline a 1 What is discriminant analysis? 目2、 Two populations discriminant analysis a 3 More than two populations discriminant analysis -distance discriminant analysis Bayes discriminant analysis Fisher discriminant analysis variable selection discriminant analysis (forward discriminant analysis) backward discriminant analysis) (stepwise discriminant analysis 2021/1/21

2021/1/21 2 cxt Presentation Outline  1、What is discriminant analysis?  2、Two populations discriminant analysis  3、More than two populations discriminant analysis －distance discriminant analysis －Bayes discriminant analysis －Fisher discriminant analysis －variable selection discriminant analysis (forward discriminant analysis) ( backward discriminant analysis) (stepwise discriminant analysis)

7.1 what is discriminant analysis 什么是判别分析? ,, Discriminant analysis is a multivariate technique that can be used to build rules according to other samples having classify information that can classify a new thing into the appropriate population. Discriminant Analysis Idea purpose Discriminant analysis(both for discrimination and classification) is a statistical technique to organize and optimize the description of differences among objects that belong to different groups or classes, and the assignment of objects of unknown class to existing classes 2021/1/21 xt

2021/1/21 3 cxt 7.1 what is discriminant analysis？ 什么是判别分析？ ❖ Discriminant analysis is a multivariate technique that can be used to build rules according to other samples having classify information that can classify a new thing into the appropriate population. ❖ Discriminant Analysis Idea & Purpose Discriminant analysis (both for discrimination and classification) is a statistical technique to organize and optimize: • the description of differences among objects that belong to different groups or classes, and • the assignment of objects of unknown class to existing classes

Thus there are two related activities or concepts in discrimination and classification Descriptive discrimination focuses on finding a few dimensions that combine the originally measured variables and that separate the classes or collections as much as possible Optimal assignment of new objects whose real grou membership is not known, into one of the existing groups or classes The basic objective of discriminant analysis: produce a rule or a classification scheme that wil enable a researcher to predict the population from which an 20>,observation is most likely to have come

2021/1/21 4 cxt ❖ Thus, there are two related activities or concepts in discrimination and classification: • Descriptive discrimination focuses on finding a few dimensions that combine the originally measured variables and that separate the classes or collections as much as possible. • Optimal assignment of new objects, whose real group membership is not known, into one of the existing groups or classes. ❖ The basic objective of discriminant analysis: produce a rule or a classification scheme that will enable a researcher to predict the population from which an observation is most likely to have come

◆判别分析 根据已知对象的某当观测指标和所属类别来判断未知对象所属 类 今判别分析的基本思想 1,是根据 本的 数据及所属类别 的信意,总结骸事物分类的规律性,雞判别公式和判别准则。 2、根据总结出来的判别公式和判别准则,判别未知类别的样本点 所属的类别。 判别分析的目的:识别一个个体所属类别 2021/1/21 cXt

2021/1/21 5 cxt ❖ 判别分析 根据已知对象的某些观测指标和所属类别来判断未知对象所属 类别的一种统计学方法。 ❖ 判别分析的基本思想 １、是根据已掌握的、历史上若干样本的p个指标数据及所属类别 的信息，总结出该事物分类的规律性，建立判别公式和判别准则。 2、根据总结出来的判别公式和判别准则，判别未知类别的样本点 所属的类别。 判别分析的目的：识别一个个体所属类别

Applications Discriminant Analysis(判别分 析的应用:无处不在) a The marketing manager of a consumer packaged goods firm is interested in identifying salient attributes that successfully differentiate between purchasers and nonpurchasers of brands, and employing this information to predict purchase intentions of potential customers a we consider a bank officer who wishes to decide whether the applicant's characteristics are more like those of persons in the past who repaid loans successfully than like those of persons who defaulted 2021/1/21

2021/1/21 6 cxt ❖ Applications Discriminant Analysis (判别分 析的应用：无处不在)  The marketing manager of a consumer packaged goods firm is interested in identifying salient attributes that successfully differentiate between purchasers and nonpurchasers of brands, and employing this information to predict purchase intentions of potential customers  we consider a bank officer who wishes to decide whether the applicant’s characteristics are more like those of persons in the past who repaid loans successfully than like those of persons who defaulted

a For example, we may want to determine what characteristics best discriminate between good and bad credit card customers a For example, a student applying to go to college may have to be classified as likely to succeed or likely to fail based on the characteristics of students who did succeed or fail in the past 2021/1/21 cXt

2021/1/21 7 cxt  For example, we may want to determine what characteristics best discriminate between good and bad credit card customers.  For example, a student applying to go to college may have to be classified as likely to succeed or likely to fail based on the characteristics of students who did succeed or fail in the past

口经济学 口例1:中小企业的破产模型 为了硏究中小企业的破产模型,选定4个经济指标: X1总负债率(现金收益/总负债) X2收益性指标(纯收入/总财产) X3短期支付能力(流动资产/流动负债) X4生产效率性指标(流动资产/纯销售额) 对17个破产企业(1类)和21个正常运行企业(2类)进 行了调查,得如下资料 2021/1/21

2021/1/21 8 cxt  经济学：  例1：中小企业的破产模型 为了研究中小企业的破产模型，选定4个经济指标： X1总负债率（现金收益/总负债） X2收益性指标（纯收入/总财产） X3短期支付能力（流动资产/流动负债） X4生产效率性指标（流动资产/纯销售额） 对17个破产企业（1类）和21个正常运行企业（2类）进 行了调查，得如下资料：

总负债率收益性指标短期支付能力生产效率指标 类别 45 41 109 56 31 151 16 09 145 26 10 09 156 67 71 28 23 30 22 18 02 131 25 2,15 70 28 23 119 66 15 05 188 27 199 38 08 08 151 42 05 168 95 1.26 12 114 17 28 27 1.27 ,51 51 10 2.49 2 02 2.01 3 2 2021/1/21 cXt

2021/1/21 9 cxt 总负债率 收益性指标 短期支付能力 生产效率指标 类别 -.45 -.41 1.09 .45 1 -.56 -.31 1.51 .16 1 .06 .02 1.01 .40 1 -.07 -.09 1.45 .26 1 -.10 -.09 1.56 .67 1 -.14 -.07 .71 .28 1 -.23 -.30 .22 .18 1 .07 .02 1.31 .25 1 .01 .00 2.15 .70 1 -.28 -.23 1.19 .66 1 .15 .05 1.88 .27 1 .37 .11 1.99 .38 1 -.08 -.08 1.51 .42 1 .05 .03 1.68 .95 1 .01 .00 1.26 .60 1 .12 .11 1.14 .17 1 -.28 -.27 1.27 .51 1 .51 .10 2.49 .54 2 .08 .02 2.01 .53 2

3.27 55 19 05 2.25 33 32 07 4.24 ,63 69 12 05 2.52 69 02 02 2.05 35 22 08 2.35 L∩ 17 07 1.80 52 15 05 2.17 10 1.01 2.50 58 ,14 03 14 07 2,61 52 33 09 3.01 47 1.24 18 56 4,29 45 2222222222222222222 20 08 1.99 30 47 14 45 17 04 2.45 14 58 04 5.06 13 04 01 1.50 待判 2021/1/21-,06 ,06 1Q.37 40 待判 cXt

2021/1/21 10 cxt .38 .11 3.27 .55 2 .19 .05 2.25 .33 2 .32 .07 4.24 .63 2 .31 .05 4.45 .69 2 .12 .05 2.52 .69 2 -.02 .02 2.05 .35 2 .22 .08 2.35 .40 2 .17 .07 1.80 .52 2 .15 .05 2.17 .55 2 -.10 -1.01 2.50 .58 2 .14 -.03 .46 .26 2 .14 .07 2.61 .52 2 -.33 -.09 3.01 .47 2 .48 .09 1.24 .18 2 .56 .11 4.29 .45 2 .20 .08 1.99 .30 2 .47 .14 2.92 .45 2 .17 .04 2.45 .14 2 .58 .04 5.06 .13 2 .04 .01 1.50 .71 待判 -.06 -.06 1.37 .40 待判